Question

What is the vertex of the quadratic function f(x) = (x – 6)(x + 2)?

Answer 1

The vertex is (2,-16)

Explanation:

The given function is
`f(x)=(x-6)(x+2)`

We expand to obtain;

`f(x)=x^2+2x-6x-12`

`f(x)=x^2-4x-12`

We complete the squares to obtain;

`f(x)=x^2-4x+(-2)^2-12-(-2)^2`

`f(x)=x^2-4x+(-2)^2-12-4`

`f(x)=(x-2)^2-16`

The vertex form is
`f(x)=(x-2)^2-16`

Comparing this to

`f(x)=a(x-k)^2+k`

The vertex is (h,k)= (2,-16)